Now that you have seen how to solve for force and the acceleration of gravity using Newton's Universal Law of Gravitation, now it is time to practice solving some problems on your own. Use what you know to solve the following problems.
| Problem | Picture | Given/Find | Equation | Solution |
|---|---|---|---|---|
| Find the force of gravity between you (60.0 kg) and the moon (7.36 x 1022 kg) at 3.84 x 108 m. |
|
\(\small\mathsf{ m_1 = 60.0 \text{ kg} }\) \(\small\mathsf{ m_2 = 7.36 \times 10^{22} \text{ kg} }\) \(\small\mathsf{ r = 3.84 \times 10^{8} \text{ m}}\) |
\(\small\mathsf{ F_g = \frac{Gm_1m_2}{r^2} }\) | \(\small\mathsf{ F_g = \frac{(6.673 \times 10^{-11} \text{ Nm}^2 \text{/kg}^2)(60.0 \text{ kg})(7.36 \times 10^{22} \text{ kg})}{(3.84 \times 10^{8} \text{ m})^2} }\) \(\small\mathsf{ F_g = 2.00 \times 10^{-3} \text{ N} }\) |
| Imagine two students standing near one another in a classroom. What is the mass of a student if the magnitude of the gravitational force acting on a 65.0 kg student who is sitting 2.25 m away is 8.29 x 10-8 N? |
|
\(\small\mathsf{ m_1 = 65.0 \text{ kg} }\) \(\small\mathsf{ m_2 = ? \text{ kg} }\) \(\small\mathsf{ r = 2.25 \text{ m}}\) \(\small\mathsf{ F_g = 8.29 \times 10^{-8} \text{ N} }\) |
\(\small\mathsf{ F_g = \frac{Gm_1m_2}{r^2} }\) | \(\small\mathsf{ 8.29 \times 10^{-8} \text{ N} = \frac{(6.673 \times 10^{-11} \text{ Nm}^2 \text{/kg}^2)(65.0 \text{ kg})m_2}{(2.25 \text{ m})r^2} }\) \(\small\mathsf{ 4.197 \times 10^{-7} \text{ Nm}^2 = (4.33 \times 10^{-9} \text{ Nm}^2 \text{/kg})m_2 }\) \(\small\mathsf{ m_2 = 96.9 \text{ kg} }\) |
| Find the acceleration due to gravity on an astronaut who is 275 km above the surface of Mars. (\(\small\mathsf{ m_{Mars} = 6.39 \times 10^{23} \text{ kg} }\) and \(\small\mathsf{ r_{Mars} = 3.39 \times 10^{6} \text{ m} }\)) |
|
\(\small\mathsf{ M = 6.39 \times 10^{23} \text{ kg} }\) \(\small\mathsf{ r = 3.39 \times 10^{6} \text{ m}}\) |
\(\small\mathsf{ g = \frac{GM}{r^2} }\) | \(\small\mathsf{ g = \frac{(6.673 \times 10^{-11} \text{ Nm}^2 \text{/kg}^2)(6.39 \times 10^{23} \text{ kg})}{(3.39 \times 10^{6} \text{ m} + 2.75 \times 10^{5})^2} }\) \(\small\mathsf{ g = 3.17 \text{ m/s}^2 }\) |
